## OP-SF WEB

### Extract from OP-SF NET

Topic #10 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor (muldoon@yorku.ca)
Subject: Book on Orthogonal Polynomial for Exponential Weights
[From the Springer Mathematics Newsletter]
Forthcoming:
A.L. Levin, The Open University of Israel, Tel Aviv, and
Doron S. Lubinsky, Witwatersrand University, Wits, South Africa
Orthogonal Polynomial for Exponential Weights
CMS Books in Mathematics, Vol 4
2000. Approx. 350 pp. Hardcover $69.95 (tent.) ISBN 0-387-98941-2
The analysis of orthogonal polynomials associated with general weights has
been a major theme in classical analysis this century. The use of
potential theory since the early 1980's has had a dramatic influence on
the development of orthogonal polynomials associated with weights on the
real line. For many applications of orthogonal polynomials, for example in
approximation theory and numerical analysis, it is not asymptotics but
certain bounds that are most important.
In this monograph, the authors define and discuss their classes of
weights, state several of their results on Christoffel functions,
Bernstein inequalities, restricted range inequalities, and record their
bounds on the orthogonal polynomials as well as their asymptotic results.
This book will be of interest to researchers in approximation theory and
potential theory, as well as in some branches of engineering.

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